Testing the equality of the laws of two strictly stationary processes

Denys Pommeret (), Laurence Reboul and Anne-francoise Yao
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Denys Pommeret: ISFA
Laurence Reboul: Aix-Marseille University
Anne-francoise Yao: Clermont Auvergne University

Statistical Inference for Stochastic Processes, 2023, vol. 26, issue 1, No 7, 193-214

Abstract: Abstract In this paper we consider the problem of comparison of two strictly stationary processes. The novelty of our approach is that we consider all their d-dimensional joint distributions, for $$d\geqslant 1$$ d ⩾ 1 . Our procedure consists in expanding their densities in a multivariate orthogonal basis and comparing their k first coefficients. The dimension d to consider and the number k of coefficients to compare in view of performing the test can growth with the sample size and are automatically selected by a two-step data-driven procedure. The method works for possibly paired, short or long range dependent processes. A simulation study shows the good behavior of the test procedure. In particular, we apply our method to compare ARFIMA processes. Some real-life applications also illustrate this approach.

Keywords: Goodness-of-fit test; Orthogonal polynomials; Stationary process; Smooth test; Two step data-driven procedure (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11203-022-09272-w

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